Question

x=r cos A . sin B , y = r cos A . cos B and z= r sin A , then x²+y²+z²=

Answer 1

Ans is r^2
Sol substituting x y z and rearranging we get r^2cos^A(sin^2B+cos^2B)+r^2sin^2B

Answer 2

x^2+y^2+z^2=
r^2cos^2Asin^2B+r^2cos^2Acos^2B+r^2sin^2A
here r^2cos^2A taken as common...
=r^2cos^2A(sin^2B+cos^2B)+r^2sin^2A
as we know sin^2B+cos^2B=1
=r^2cos^2A(1)+r^2sin^2A
=r^2(cos^2A+sin^2A)
=r^2
therefore x^2+y^2+z^2=r^2
hope it helps friend...